BRST symmetry vs. Horizon condition in Yang-Mills theories

TL;DR

This paper explores the relationship between lattice gluon propagators in different gauges in SU(2) Yang-Mills theories and discusses the implications for confinement mechanisms and BRST symmetry.

Contribution

It establishes a simple relation between Coulomb and Landau gauge gluon propagators and analyzes the impact on the BRST symmetry and confinement criteria in Yang-Mills theories.

Findings

A relation exists between Coulomb and Landau gauge gluon propagators.

The realization of the Gribov-Zwanziger confinement mechanism affects BRST charge definition.

The Kugo-Ojima criterion may not hold non-perturbatively due to BRST issues.

Abstract

We show that in SU(2) Yang-Mills theories a simple relation exists between lattice gluon propagators in Coulomb and Landau gauge and discuss the physical implications of such result. In particular, the realization of the Gribov-Zwanziger confinement mechanism in Coulomb gauge, linked to dual-superconductivity, would imply that the standard BRST charge must be ill defined non perturbatively. As a consequence, the Kugo-Ojima confinement criterion, which relies on BRST charge conservation beyond perturbation theory, would not be fulfilled.